






'''simple docstring'''







import unittest

import numpy as np

from transformers.testing_utils import require_flax, require_tf, require_torch
from transformers.utils import (
    expand_dims,
    flatten_dict,
    is_flax_available,
    is_tf_available,
    is_torch_available,
    reshape,
    squeeze,
    transpose,
)


if is_flax_available():
  import jax.numpy as jnp

if is_tf_available():
  import tensorflow as tf

if is_torch_available():
  import torch




class   __SCREAMING_SNAKE_CASE       (unittest.TestCase       ):


  """simple docstring"""


  def    _a       (			self	):






         """simple docstring"""


         a_						     =			{
             'task_specific_params': {
                 'summarization': {'length_penalty': 1.0, 'max_length': 128, 'min_length': 12, 'num_beams': 4},
                 'summarization_cnn': {'length_penalty': 2.0, 'max_length': 142, 'min_length': 56, 'num_beams': 4},
                 'summarization_xsum': {'length_penalty': 1.0, 'max_length': 62, 'min_length': 11, 'num_beams': 6},
             }
         }
         a_						     =			{
             'task_specific_params.summarization.length_penalty': 1.0,
             'task_specific_params.summarization.max_length': 128,
             'task_specific_params.summarization.min_length': 12,
             'task_specific_params.summarization.num_beams': 4,
             'task_specific_params.summarization_cnn.length_penalty': 2.0,
             'task_specific_params.summarization_cnn.max_length': 142,
             'task_specific_params.summarization_cnn.min_length': 56,
             'task_specific_params.summarization_cnn.num_beams': 4,
             'task_specific_params.summarization_xsum.length_penalty': 1.0,
             'task_specific_params.summarization_xsum.max_length': 62,
             'task_specific_params.summarization_xsum.min_length': 11,
             'task_specific_params.summarization_xsum.num_beams': 6,
         }

         self.assertEqual(flatten_dict(UpperCamelCase__	)   ,	UpperCamelCase__	)







  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__	)   ,	x.transpose()	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__   ,	axes=(1, 2, 0)	)   ,	x.transpose((1, 2, 0)	)	)	)







  @require_torch
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			torch.tensor(UpperCamelCase__	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__	)   ,	transpose(UpperCamelCase__	).numpy()	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         a_						     =			torch.tensor(UpperCamelCase__	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__   ,	axes=(1, 2, 0)	)   ,	transpose(UpperCamelCase__   ,	axes=(1, 2, 0)	).numpy()	)	)







  @require_tf
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			tf.constant(UpperCamelCase__	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__	)   ,	transpose(UpperCamelCase__	).numpy()	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         a_						     =			tf.constant(UpperCamelCase__	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__   ,	axes=(1, 2, 0)	)   ,	transpose(UpperCamelCase__   ,	axes=(1, 2, 0)	).numpy()	)	)







  @require_flax
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			jnp.array(UpperCamelCase__	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__	)   ,	np.asarray(transpose(UpperCamelCase__	)	)	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         a_						     =			jnp.array(UpperCamelCase__	)
         self.assertTrue(np.allclose(transpose(UpperCamelCase__   ,	axes=(1, 2, 0)	)   ,	np.asarray(transpose(UpperCamelCase__   ,	axes=(1, 2, 0)	)	)	)	)







  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(4, 3)	)   ,	np.reshape(UpperCamelCase__   ,	(4, 3)	)	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(12, 5)	)   ,	np.reshape(UpperCamelCase__   ,	(12, 5)	)	)	)







  @require_torch
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			torch.tensor(UpperCamelCase__	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(4, 3)	)   ,	reshape(UpperCamelCase__   ,	(4, 3)	).numpy()	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         a_						     =			torch.tensor(UpperCamelCase__	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(12, 5)	)   ,	reshape(UpperCamelCase__   ,	(12, 5)	).numpy()	)	)







  @require_tf
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			tf.constant(UpperCamelCase__	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(4, 3)	)   ,	reshape(UpperCamelCase__   ,	(4, 3)	).numpy()	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         a_						     =			tf.constant(UpperCamelCase__	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(12, 5)	)   ,	reshape(UpperCamelCase__   ,	(12, 5)	).numpy()	)	)







  @require_flax
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			jnp.array(UpperCamelCase__	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(4, 3)	)   ,	np.asarray(reshape(UpperCamelCase__   ,	(4, 3)	)	)	)	)

         a_						     =			np.random.randn(3   ,	4   ,	5	)
         a_						     =			jnp.array(UpperCamelCase__	)
         self.assertTrue(np.allclose(reshape(UpperCamelCase__   ,	(12, 5)	)   ,	np.asarray(reshape(UpperCamelCase__   ,	(12, 5)	)	)	)	)







  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(1   ,	3   ,	4	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__	)   ,	np.squeeze(UpperCamelCase__	)	)	)

         a_						     =			np.random.randn(1   ,	4   ,	1   ,	5	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__   ,	axis=2	)   ,	np.squeeze(UpperCamelCase__   ,	axis=2	)	)	)







  @require_torch
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(1   ,	3   ,	4	)
         a_						     =			torch.tensor(UpperCamelCase__	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__	)   ,	squeeze(UpperCamelCase__	).numpy()	)	)

         a_						     =			np.random.randn(1   ,	4   ,	1   ,	5	)
         a_						     =			torch.tensor(UpperCamelCase__	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__   ,	axis=2	)   ,	squeeze(UpperCamelCase__   ,	axis=2	).numpy()	)	)







  @require_tf
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(1   ,	3   ,	4	)
         a_						     =			tf.constant(UpperCamelCase__	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__	)   ,	squeeze(UpperCamelCase__	).numpy()	)	)

         a_						     =			np.random.randn(1   ,	4   ,	1   ,	5	)
         a_						     =			tf.constant(UpperCamelCase__	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__   ,	axis=2	)   ,	squeeze(UpperCamelCase__   ,	axis=2	).numpy()	)	)







  @require_flax
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(1   ,	3   ,	4	)
         a_						     =			jnp.array(UpperCamelCase__	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__	)   ,	np.asarray(squeeze(UpperCamelCase__	)	)	)	)

         a_						     =			np.random.randn(1   ,	4   ,	1   ,	5	)
         a_						     =			jnp.array(UpperCamelCase__	)
         self.assertTrue(np.allclose(squeeze(UpperCamelCase__   ,	axis=2	)   ,	np.asarray(squeeze(UpperCamelCase__   ,	axis=2	)	)	)	)







  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         self.assertTrue(np.allclose(expand_dims(UpperCamelCase__   ,	axis=1	)   ,	np.expand_dims(UpperCamelCase__   ,	axis=1	)	)	)







  @require_torch
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			torch.tensor(UpperCamelCase__	)
         self.assertTrue(np.allclose(expand_dims(UpperCamelCase__   ,	axis=1	)   ,	expand_dims(UpperCamelCase__   ,	axis=1	).numpy()	)	)







  @require_tf
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			tf.constant(UpperCamelCase__	)
         self.assertTrue(np.allclose(expand_dims(UpperCamelCase__   ,	axis=1	)   ,	expand_dims(UpperCamelCase__   ,	axis=1	).numpy()	)	)







  @require_flax
  def    _a       (			self	):






         """simple docstring"""


         a_						     =			np.random.randn(3   ,	4	)
         a_						     =			jnp.array(UpperCamelCase__	)
         self.assertTrue(np.allclose(expand_dims(UpperCamelCase__   ,	axis=1	)   ,	np.asarray(expand_dims(UpperCamelCase__   ,	axis=1	)	)	)	)












'''simple docstring'''







def       __UpperCamelCase					(      lowercase_       :  int = 1_000_000   ):
       """simple docstring"""




       a_						     =			set(range(3   ,       lowercase_   ,       2   )   )
       primes.add(2   )
       for p in range(3   ,       lowercase_   ,       2   ):
              if p not in primes:
                     continue
              primes.difference_update(set(range(p * p   ,       lowercase_   ,       lowercase_   )   )   )

       a_						     =			[float(lowercase_   ) for n in range(limit + 1   )]

       for p in primes:
              for n in range(lowercase_   ,       limit + 1   ,       lowercase_   ):
                     phi[n] *= 1 - 1 / p

       return int(sum(phi[2:]   )   )


if __name__ == "__main__":
  print(f"""{solution() = }""")




